For each perfectly competitive firm operating in the long run, which equality correctly holds between price and cost measures?

Introduction / Context:
This question examines your understanding of the long run equilibrium of a perfectly competitive firm in microeconomics. Perfect competition is a benchmark market structure where many small firms sell identical products and no single firm can influence the price. In the long run, firms adjust their output and scale so that economic profits are driven to zero and a specific cost condition holds at the chosen output level.

Given Data / Assumptions:

• The market structure is perfect competition.
• The time horizon is the long run, when firms can adjust all inputs.
• We must compare price with marginal and average costs.
• Standard textbook assumptions about cost curves and free entry are implied.

Concept / Approach:
In a perfectly competitive market, each firm is a price taker, so price equals marginal revenue. Profit maximisation requires producing where marginal cost equals marginal revenue, so in equilibrium price equals marginal cost. In the long run, free entry and exit ensure that firms earn only normal profit, which happens when price equals minimum average total cost. Therefore, in long run equilibrium we have price equals marginal cost equals minimum average total cost.

Step-by-Step Solution:
Step 1: Recall that in perfect competition marginal revenue equals price at all output levels.Step 2: For profit maximisation, the firm sets output where marginal cost equals marginal revenue.Step 3: Combine these facts to get price equals marginal cost at the chosen output.Step 4: In the long run, entry and exit drive economic profit to zero, which occurs when price equals average total cost.Step 5: At the efficient scale in this market, the firm produces where average total cost is at its minimum, so price equals marginal cost equals minimum average total cost.

Verification / Alternative Check:
Standard microeconomics diagrams of long run equilibrium for a perfectly competitive firm show the horizontal demand curve at the point where it is tangent to the firm average total cost curve at its minimum point and also intersects the marginal cost curve. The tangency and intersection points confirm that price equals marginal cost and equals minimum average total cost simultaneously. This visual confirmation matches the statement in option C.

Why Other Options Are Wrong:
Option A equates price, marginal cost and average variable cost, but in long run equilibrium it is the average total cost, not only the variable part, that equals price. Option B is incorrect because price is not equal to average profit; average profit is zero in long run competitive equilibrium, while price is positive. Option D is incomplete, as minimum average variable cost does not capture fixed costs and does not represent the true long run equilibrium condition. Thus, only option C correctly states the equality that holds.

Common Pitfalls:
Candidates sometimes confuse average variable cost with average total cost, especially when thinking about shutdown decisions. They may also forget that in the long run all costs are variable, which shifts focus to total cost measures. Another mistake is to think that any point where marginal cost equals average cost is automatically efficient; in fact, it must be at the minimum of the average total cost curve. Keeping these distinctions clear will help in solving similar questions.

Final Answer:
For a perfectly competitive firm in the long run, price equals marginal cost and also equals minimum average total cost.